1. Field of the Invention
The present invention relates to a power supply device that supplies power to a load by utilizing a magnetic coupling between coils.
2. Description of the Related Art
Methods to supply power to a load utilizing a magnetic coupling mutually between coils by electromagnetic induction include, for example, non-contact power supply. The principle thereof is forming a so-called transformer by magnetically coupling a plurality of coils through a space, and utilizing the electromagnetic induction between the coils, thereby exchanging power.
For example, the method includes arranging a primary side coil that corresponds to a power supply source as a power supply line in a rail shape, integrating a secondary side coil with a power receiving circuit to form a mobile object, and at the same time, making the primary side coil and the secondary side coil be opposed to each other. With this, it is possible to conduct a non-contact power supply to a mobile object that moves along the power supply line.
Here, FIG. 8 illustrates a non-contact power supply device described in Japanese Laid-open Patent Publication No. 2002-354711. In FIG. 8, to both ends of a high-frequency power source 100, a primary side power supply line 110 is connected as a coil. To the primary side power supply line 110, a power receiving coil 120 is coupled magnetically, and the primary side power supply line 110 and the power receiving coil 120 form a sort of a transformer.
Both ends of the power receiving coil 120 are connected to a pair of AC (alternating-current) terminals of a full-wave rectifier circuit 10 through a resonance capacitor Cr. The power receiving coil 120 and the resonance capacitor Cr form a serial resonance circuit.
The full-wave rectifier circuit 10 is formed by bridge-connecting diodes Du, Dv, Dx, and Dy. To a pair of DC (direct-current) terminals of the full-wave rectifier circuit 10, a constant voltage control circuit 20 is connected that controls a DC output voltage of the full-wave rectifier circuit 10 to be a reference voltage value. The constant voltage control circuit 20 is formed of a step-up chopper circuit that is formed, for example, of a reactor L1, a diode D1, a smoothing capacitor C0, and a semiconductor switch SW1. Further, to both ends of the smoothing capacitor C0, a load R is connected.
In FIG. 8, a control device that switches a semiconductor switch SW1 is omitted.
In the conventional technology disclosed in FIG. 8, a high-frequency current is applied to the primary side power supply line 110 by the high frequency power source 100 and the high-frequency power supplied through the power receiving coil 120 is input into the full-wave rectifier circuit 10 to convert it into DC power.
Generally, in this type of a non-contact power supply device, due to a change in a gap length between the primary side power supply line 110 and the power receiving coil 120, or a position gap of both, a voltage induced in the power receiving coil 120 changes. As a result of this, the DC output voltage of the full-wave rectifier circuit 10 changes. Further, characteristics of the load R also cause the DC output voltage of the full-wave rectifier circuit 10 to change. Accordingly, in FIG. 8, the DC output voltage of the full-wave rectifier circuit 10 is controlled to have a constant value by the constant voltage control circuit 20.
In the non-contact power supply device, the higher the frequency of the current supplied through a coil, the smaller an excitation inductance needed for transmitting a power, and a size of a coil or a core arranged at a periphery of the coil may be made to be small. However, in a power converter which forms a high frequency power source device or a power receiving circuit, the higher the frequency of the current flowing through the circuit, the larger an increase in a switching loss of a semiconductor switch, and a power supply efficiency lowers. Accordingly, it is common to set the frequency of the power supplied in a non-contact state to several [kHz] to several tens of [kHz].
In the non-contact power supply device illustrated in FIG. 8, in particular, a power receiving circuit in a subsequent stage of the resonance capacitor Cr has the following problems.
(1) Since the power receiving circuit is configured by the full-wave rectifier circuit 10 and the constant voltage control circuit 20, a size of an entire circuit becomes large and it causes an increase in installation space or cost.
(2) Since losses occur not only in the diodes Du, Dv, Dx, and Dy of the full-wave rectifier circuit 10 but also in the reactor L1, the semiconductor switch SW1, and the diode D1 of the constant voltage control circuit 20, these losses cause a reduction in a power supply efficiency.
As a conventional technology that solves the problems above, inventors have proposed a non-contact power supply device and a method for controlling the same as described in Japanese Laid-open Patent Publication No. 2012-125138.
FIG. 9 illustrates a non-contact power supply device described in Japanese Laid-open Patent Publication No. 2012-125138. In FIG. 9, 310 is a power receiving circuit. The power receiving circuit 310 includes semiconductor switches Qu, Qx, Qv, and Qy, diodes Du, Dx, Dv, and Dy, and a smoothing capacitor C0. The semiconductor switches Qu, Qx, Qv, and Qy are bridge-connected. The diodes Du, Dx, Dv, and Dy are connected in inverse-parallel to the switches Qu, Qx, Qv, and Qy, respectively. The capacitors Cx and Cy are respectively connected in parallel to the switches Qx and Qy of a lower arm. The smoothing capacitor C0 is connected between DC terminals of a bridge circuit being formed of these elements. A series circuit of a resonance capacitor Cr and a power receiving coil 120 is connected between AC terminals of the bridge circuit, and a load R is connected to both ends of the smoothing capacitor C0.
200 is a control device that generates a driving signal for switching the semiconductor switches Qu, Qx, Qv, and Qy. The control device 200 generates the above mentioned driving signal on the basis of a current i of the power receiving coil 120 detected by a current detection unit CT and a voltage Vo between DC terminals (DC output voltage) of the power receiving circuit 310.
In the non-contact power supply device, by controlling the semiconductor switches Qu, Qx, Qv, and Qy, a voltage v between the AC terminals of the bridge circuit is controlled to be a positive-negative voltage whose peak value is the voltage Vo between the DC terminals. A power supplied from a primary side power supply line 110 to the power receiving circuit 310 is a product of the current i of the power receiving coil 120 and the voltage v between the AC terminals. The control device 200 adjusts a phase of driving signals of the semiconductor switches Qu, Qx, Qv, and Qy on the basis of the voltage Vo between the DC terminals such that a control of the supplied power, that is, a constant control of the voltage Vo between the DC terminals, becomes available. Further, by configuring the power receiving circuit 310 using the bridge circuit which is formed of the switches Qu, Qx, Qv, and Qy and the diodes Du, Dx, Dv, and Dy, an operation of keeping the power constant is available even when the load R is a regenerative load.
According to this non-contact power supply device, the voltage Vo between the DC terminals may be controlled in a constant state by a phase control of the driving signals of the semiconductor switches Qu, Qx, Qv, and Qy without using a constant voltage control circuit, as illustrated in FIG. 8. In addition, the power receiving circuit 310 may be configured only of the bridge circuit and the smoothing capacitor C0. Therefore, a circuit configuration may be simplified, the size and the cost thereof may be reduced, and further, losses may be reduced by reducing the number of component parts, and consequently, a highly efficient and stable non-contact power supply may become available. In addition, by a charging/discharging action of the capacitors Cx and Cy, a so-called soft-switching is performed so as to reduce switching losses and further improve an efficiency.
However, in the conventional technology described in Japanese Laid-open Patent Publication No. 2012-125138, the current i of the power receiving coil 120 becomes a leading phase to a fundamental wave component of the voltage v between the AC terminals. Therefore, there is a problem that the input power factor of the power receiving circuit 310 reduces, and the problem invites an increase in a loss throughout the entire device and causes obstructions in further downsizing of the entire device.
In view of the foregoing, the applicant has proposed a non-contact power supply device in which an input power factor of a power receiving circuit has been improved (hereinafter referred to as a “first prior application invention”) as described in Japanese Laid-open Patent Publication No. 2013-071432.
FIG. 10 is a circuit diagram of the first prior application invention. In FIG. 10, a power receiving circuit 320 includes semiconductor switches Qu, Qx, Qv, and Qy, diodes Du, Dx, Dv, and Dy, and a smoothing capacitor C0. The semiconductor switches Qu, Qx, Qv, and Qy are bridge-connected. The diodes Du, Dx, Dv, and Dy are respectively connected in inverse-parallel to the switches Qu, Qx, Qv, and Qy. The smoothing capacitor C0 is connected between a pair of DC terminals of abridge circuit being formed of these elements. A series circuit of a resonance capacitor Cr and a power receiving coil 120 is connected between a pair of AC terminals of the bridge circuit, and a load R is connected to both ends of the smoothing capacitor C0. Here, 100 is a high frequency power source, and 110 is a primary side power supply line.
On the other hand, a control device 200 generates driving signals of the switches Qu, Qx, Qv, and Qy on the basis of a voltage Vo between the DC terminals and a current i of the power receiving coil 120 detected by a current detection unit CT and outputs the driving signals. Although it is not illustrated, the voltage Vo between the DC terminals is detected by a well-known voltage detection unit such as a DC voltage detector.
Described next is an operation when power is supplied from the power receiving coil 120 to the load R in FIG. 10.
FIG. 11 illustrates a current i that flows through the power receiving coil 120, a voltage v between the AC terminals of the bridge circuit, a fundamental wave component v′ of the voltage v, and driving signals of the switches Qu, Qx, Qv, and Qy. The switches Qu, Qx, Qv, and Qy perform a switching operation with a constant frequency synchronized with the current i. In FIG. 11, a ZCP′ represents a zero crossing point of the current i. Described below is an operation in each time period (1) to (4) of FIG. 11.    (1) Time period (1) (switches Qu and Qy are turned on): The current i flows with a route of a receiving coil 120→a resonance capacitor Cr→a diode Du→a smoothing capacitor C0→a diode Dy→the power receiving coil 120. The voltage v between the AC terminals becomes a positive voltage whose peak value is a voltage Vo between DC terminals. During this time period, a smoothing capacitor C0 is charged by the current i.    (2) Time period (2) (switches Qx and Qy are turned on): The current i flows with a route of a receiving coil 120→a resonance capacitor Cr→a switch Qx→a diode Dy→the power receiving coil 120. The voltage v between the AC terminals becomes a zero voltage.    (3) Time period (3) (switches Qu and Qv are turned on): The current i flows with a route of a resonance capacitor Cr→a power receiving coil 120→a diode Dv→a switch Qu→the resonance capacitor Cr. The voltage v between the AC terminals becomes a zero voltage.    (4) Time period (4) (switches Qx and Qv are turned on): The current i flows with a route of a resonance capacitor Cr→a power receiving coil 120→a diode Dv→a smoothing capacitor C0→a diode Dx→the resonance capacitor Cr. The voltage v between the AC terminals becomes a negative voltage whose peak value is the voltage Vo between the DC terminals. During this time period, the smoothing capacitor C0 is charged by the current i.
Hereafter, operations are transitioned to a switching mode of the time period (1), and similar operations are repeated.
As is clear from FIG. 11, the control device 200 performs a switching control of the semiconductor switches Qu, Qx, Qv, and Qy. Consequently, the voltage v between the AC terminals is controlled such that the voltage v becomes a zero voltage only during time periods α before and after one of two zero crossing points ZCP′ of the current i that flows through the power receiving coil 120 and such that the voltage v becomes a positive-negative voltage whose peak value is the voltage Vo between the DC terminals during the other time periods. A power supplied from the primary side power supply line 110 to the power receiving circuit 320 is a product of the current i and the voltage v. Accordingly, the control device 200 adjusts the driving signals of the switches Qu, Qx, Qv, and Qy on the basis of a detected value of the voltage Vo between the DC terminals such that a control of the supplied power, that is, a constant control of the voltage Vo between the DC terminals, becomes available.
When this happens, as illustrated in FIG. 11, since a phase difference between the current i and the fundamental wave component v′ of the voltage v between the AC terminals becomes 0°, an input power factor of the power receiving circuit 320 may be set to 1.
Here, in the first prior application invention, when resonance frequency of the power receiving coil 120 and the resonance capacitor Cr completely coincides with a power source frequency, the input power factor of the power receiving circuit 320 becomes 1, but when the resonance frequency deviates from the power source frequency, the input power factor of the power receiving circuit 320 is decreased. The reason for that is described below.
FIG. 12 illustrates an input side equivalent circuit of the power receiving circuit 320 in a case in which the resonance frequency of the power receiving coil 120 and the resonance capacitor Cr deviates from the power source frequency. In FIG. 12, a voltage vin induced in the power receiving coil 120 is represented as an AC power source, and the reference numeral 400 denotes an impedance that corresponds to the power receiving circuit 320 and the load R. Generally, the other impedance to the load R can be ignored, and therefore the reference numeral 400 may be regarded as a pure resistance that corresponds to the load R.
Further, FIG. 13 illustrates operating waveforms of a current i that flows through the power receiving coil 120, an induced voltage vin of the power receiving coil 120, a voltage v between AC terminals of the bridge circuit, a fundamental wave component v′ of the voltage v, and driving signals of the switches Qu, Qx, Qv, and Qy.
As illustrated in FIG. 12, inductance of the power receiving coil 120 is assumed to be L[H], and capacitance of the resonance capacitor Cr is assumed to be Cr[F] similarly to a reference numeral of the component. Further, when the power source frequency is assumed to be fs[Hz], combined inductance Ls[H] of the inductance L and the resonance conductor Cr is defined by the expression φ.
                              2          ⁢                                          ⁢          π          ⁢                                          ⁢                      f            s                    ⁢                      L            s                          =                              2            ⁢                                                  ⁢            π            ⁢                                                  ⁢                          f              s                        ⁢            L                    -                      1                          2              ⁢                                                          ⁢              π              ⁢                                                          ⁢                              f                s                            ⁢                              C                r                                                                        (        1        )            
On the other hand, a resonance frequency of a resonance circuit being formed of the power receiving coil 120 and the resonance capacitor Cr is represented by the expression (2).
                              f          c                =                  1                      2            ⁢                                                  ⁢            π            ⁢                                          LC                r                                                                        (        2        )            
Accordingly, when fc=fs, Ls=0 is established, and when fc≠fs, Ls≠0 is established.
In addition, according to the control method illustrated in FIG. 11, a phase of v′ coincides with that of i. Therefore, when the current i of the power receiving coil 120 is represented as I sin ωt, v′ is represented as V′ sin ωt.
On the other hand, vin is represented by the sum of the fundamental wave component v′ of v and vL by the circuit illustrated in FIG. 12 so as to be represented by the expression (3).
                                                                                                              V                    in                                    ⁡                                      (                                          ω                      ⁢                                                                                          ⁢                      t                                        )                                                  =                                ⁢                                                                            v                      ′                                        ⁡                                          (                                              ω                        ⁢                                                                                                  ⁢                        t                                            )                                                        +                                                            v                      L                                        ⁡                                          (                                              ω                        ⁢                                                                                                  ⁢                        t                                            )                                                                                                                                              =                                ⁢                                                                            V                      ′                                        ⁢                                          sin                      ⁡                                              (                                                  ω                          ⁢                                                                                                          ⁢                          t                                                )                                                                              +                                                            j                      ⁡                                              (                                                  2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                            s                                                                          )                                                              ⁢                                          L                      s                                        ⁢                    I                    ⁢                                                                                  ⁢                                          sin                      ⁡                                              (                                                  ω                          ⁢                                                                                                          ⁢                          t                                                )                                                                                                                                                                    =                                ⁢                                                                            V                      ′                                        ⁢                                          sin                      ⁡                                              (                                                  ω                          ⁢                                                                                                          ⁢                          t                                                )                                                                              +                                      2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                                          f                      s                                        ⁢                                          L                      s                                        ⁢                    I                    ⁢                                                                                  ⁢                                          cos                      ⁡                                              (                                                  ω                          ⁢                                                                                                          ⁢                          t                                                )                                                                                                                                                                    =                                ⁢                                                      V                    a                                    ⁢                                      sin                    ⁡                                          (                                                                        ω                          ⁢                                                                                                          ⁢                          t                                                +                        θ                                            )                                                                                                          ⁢                                  ⁢                  (                                                    V                a                            =                                                                    V                                          ′                      ⁢                                                                                          ⁢                      2                                                        +                                                            (                                              2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                          s                                                ⁢                                                  L                          s                                                ⁢                        I                                            )                                        2                                                                        ,                          θ              =                              arc                ⁢                                                                  ⁢                                  sin                  ⁡                                      (                                          2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                                              f                        s                                            ⁢                                              L                        s                                            ⁢                                              I                        /                                                  V                          a                                                                                      )                                                                                )                                    (        3        )            
When Ls=0, vin=V′ sin ωt is established, and a phase difference θ between vin and i(=I sin ωt) becomes zero, and an input power factor of the power receiving circuit 320 becomes 1. However, when Ls≠0, vin and i has a phase difference θ as illustrated in FIG. 13, and the input power factor is decreased.
In view of the foregoing, the applicant has proposed a non-contact power supply device described in Japanese Patent Application No. 2013-123810 (hereinafter referred to as a “second prior application invention”). The second prior application invention aims at improving an input power factor of a power receiving circuit even when Ls≠0, namely, when a resonance frequency of a resonance circuit being formed of a power receiving coil and a resonance capacitor does not coincide with a power source frequency.
A configuration of a circuit in the second prior application invention is similar to that of the circuit illustrated in FIG. 10, and described below is a power factor improvement operation according to the second prior application invention.
FIG. 14 illustrates operating waveforms of a current i that flows through the power receiving coil 120 in FIG. 10, an induced voltage vin of the power receiving coil 120, a voltage v between AC terminals of the bridge circuit, and a fundamental wave component v′ of the voltage v between the AC terminals of the bridge circuit, and driving signals of the switches Qu, Qx, Qv, and Qy.
In addition, FIG. 15 illustrates an input side equivalent circuit of a power receiving circuit 320 in this case, and the reference numeral 400 denotes an impedance that corresponds to the power receiving circuit 320 and a load R. Generally, the other impedance can be ignored for the load R, and therefore the reference numeral 400 can be regarded as a pure resistance that corresponds to the load R. The reference numeral 401 denotes a capacitive reactance component of v′.
In the second prior application invention, the control device 200 provides driving signals to the switches Qu, Qx, Qv, and Qy such that a middle point of a time period during which a peak value of v is 0 deviates from one zero crossing point ZCP in one cycle of the current i by a compensation period (angle) β. As a result, the input power factor of the power receiving circuit 320 is improved. According to these driving signals, the voltage v between the AC terminals has a waveform that is asymmetric with respect to the zero crossing point ZCP of i in which the voltage v is a zero voltage during time periods before and after the middle point (respectively referred to as “α”) and the voltage v is a positive-negative voltage whose peak value is a voltage V0 between DC terminals during the other periods. Accordingly, a phase of v′ deviates from a phase of i. Here, when a time period β is given such that a voltage drop caused by the capacitive reactance component 401 of v′ illustrated in FIG. 15 compensates for a voltage drop vL in Ls, the impedance of the circuit apparently becomes a pure resistance. Accordingly, as the phase of i coincides with a phase of vin, the input power factor of the power receiving circuit 320 is set to 1.
Described next is a method for obtaining the time period β for setting the input power factor to 1. First, v′ is expanded by fourier series, and is represented by the expression (4).v′(ωt)=a1 cos(ωt)+b1 sin(ωt)  (4)
From FIG. 14, a1 and b1 in the expression (4) are obtained by the expressions (5) and (6), respectively.
                                                                        a                1                            =                            ⁢                                                1                  π                                ⁢                                                      ∫                    0                                          2                      ⁢                                                                                          ⁢                      π                                                        ⁢                                                            v                      ⁡                                              (                                                  ω                          ⁢                                                                                                          ⁢                          t                                                )                                                              ⁢                                          cos                      ⁡                                              (                                                  ω                          ⁢                                                                                                          ⁢                          t                                                )                                                              ⁢                                                                                  ⁢                                          ⅆ                      ω                                        ⁢                                                                                  ⁢                    t                                                                                                                          =                            ⁢                                                                    1                    π                                    ⁢                                                            ∫                      0                                              π                        -                                                  (                                                      α                            -                            β                                                    )                                                                                      ⁢                                          V                      ⁢                                                                                          ⁢                                              cos                        ⁡                                                  (                                                      ω                            ⁢                                                                                                                  ⁢                            t                                                    )                                                                    ⁢                                                                                          ⁢                                              ⅆ                        ω                                            ⁢                                                                                          ⁢                      t                                                                      +                                                      1                    π                                    ⁢                                                            ∫                                              π                        +                                                  (                                                      α                            +                            β                                                    )                                                                                            2                        ⁢                                                                                                  ⁢                        π                                                              ⁢                                                                  (                                                  -                          V                                                )                                            ⁢                                              cos                        ⁡                                                  (                                                      ω                            ⁢                                                                                                                  ⁢                            t                                                    )                                                                    ⁢                                                                                          ⁢                                              ⅆ                        ω                                            ⁢                                                                                          ⁢                      t                                                                                                                                              =                            ⁢                                                V                  π                                ⁢                                  {                                                            sin                      ⁡                                              (                                                  α                          -                          β                                                )                                                              -                                          sin                      ⁡                                              (                                                  α                          +                          β                                                )                                                                              }                                                                                                        =                            ⁢                                                -                                                            2                      ⁢                                                                                          ⁢                      V                                        π                                                  ⁢                cos                ⁢                                                                  ⁢                α                ⁢                                                                  ⁢                sin                ⁢                                                                  ⁢                β                                                                        (        5        )                                                                                    b                1                            =                            ⁢                                                1                  π                                ⁢                                                      ∫                    0                                          2                      ⁢                                                                                          ⁢                      π                                                        ⁢                                                            V                      ⁡                                              (                                                  ω                          ⁢                                                                                                          ⁢                          t                                                )                                                              ⁢                                          sin                      ⁡                                              (                                                  ω                          ⁢                                                                                                          ⁢                          t                                                )                                                              ⁢                                                                                  ⁢                                          ⅆ                      ω                                        ⁢                                                                                  ⁢                    t                                                                                                                          =                            ⁢                                                                    1                    π                                    ⁢                                                            ∫                      0                                              π                        -                                                  (                                                      α                            -                            β                                                    )                                                                                      ⁢                                          V                      ⁢                                                                                          ⁢                                              cos                        ⁡                                                  (                                                      ω                            ⁢                                                                                                                  ⁢                            t                                                    )                                                                    ⁢                                                                                          ⁢                                              ⅆ                        ω                                            ⁢                                                                                          ⁢                      t                                                                      +                                                      1                    π                                    ⁢                                                            ∫                                              π                        +                                                  (                                                      α                            +                            β                                                    )                                                                                            2                        ⁢                                                                                                  ⁢                        π                                                              ⁢                                                                  (                                                  -                          V                                                )                                            ⁢                                              cos                        ⁡                                                  (                                                      ω                            ⁢                                                                                                                  ⁢                            t                                                    )                                                                    ⁢                                                                                          ⁢                                              ⅆ                        ω                                            ⁢                                                                                          ⁢                      t                                                                                                                                              =                            ⁢                                                V                  π                                ⁢                                  {                                      2                    +                                          cos                      ⁡                                              (                                                  α                          -                          β                                                )                                                              +                                          cos                      ⁡                                              (                                                  α                          +                          β                                                )                                                                              }                                                                                                        =                            ⁢                                                                    2                    ⁢                                                                                  ⁢                    V                                    π                                ⁢                                  (                                      1                    +                                          cos                      ⁢                                                                                          ⁢                      α                      ⁢                                                                                          ⁢                      cos                      ⁢                                                                                          ⁢                      β                                                        )                                                                                        (        6        )            
On the other hand, from FIG. 15, v′ may be represented by the expression (7).v′(ωt)=vin(ωt)−vL(ωt)  (7)
When the input power factor is set to 1, the phase of i coincides with the phase of vin, and therefore when iin(ωt)=Iin sin(ωt) is assumed, vin(ωt)=Vin sin(ωt) is established. Accordingly, the expression (7) may be represented by the expression (8).
                                                                                          v                  ′                                ⁡                                  (                                      ω                    ⁢                                                                                  ⁢                    t                                    )                                            =                            ⁢                                                                    V                    in                                    ⁢                                      sin                    ⁡                                          (                                              ω                        ⁢                                                                                                  ⁢                        t                                            )                                                                      -                                  j                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                                      L                    s                                    ⁢                  I                  ⁢                                                                          ⁢                                      sin                    ⁡                                          (                                              ω                        ⁢                                                                                                  ⁢                        t                                            )                                                                                                                                              =                            ⁢                                                                    -                    ω                                    ⁢                                                                          ⁢                                      L                    s                                    ⁢                  I                  ⁢                                                                          ⁢                                      cos                    ⁡                                          (                                              ω                        ⁢                                                                                                  ⁢                        t                                            )                                                                      +                                                      V                    in                                    ⁢                                      sin                    ⁡                                          (                                              ω                        ⁢                                                                                                  ⁢                        t                                            )                                                                                                                              (        8        )            
When putting VL=ωLsI, the expressions (9) and (10) are established by the expressions (4)-(6) and (8).
                              a          1                =                                            -                                                2                  ⁢                                                                          ⁢                  V                                π                                      ⁢            cos            ⁢                                                  ⁢            α            ⁢                                                  ⁢            sin            ⁢                                                  ⁢            β                    =                      -                          V              L                                                          (        9        )                                          b          1                =                                                            2                ⁢                                                                  ⁢                V                            π                        ⁢                          (                              1                +                                  cos                  ⁢                                                                          ⁢                  α                  ⁢                                                                          ⁢                  cos                  ⁢                                                                          ⁢                  β                                            )                                =                      V            in                                              (        10        )            
Accordingly, β and α at the time of setting the input power factor to 1 are obtained by the expressions (11) and (12), respectively.
                    β        =                              tan                          -              1                                (                      -                                          V                L                                                                                  2                    ⁢                                                                                  ⁢                    V                                    π                                -                                  V                  in                                                              )                                    (        11        )                                α        =                              cos                          -              1                                ⁡                      (                                          π                ⁢                                                                  ⁢                                  V                  L                                                            2                ⁢                                                                  ⁢                V                ⁢                                                                  ⁢                sin                ⁢                                                                  ⁢                β                                      )                                              (        12        )            
Namely, even when the power source frequency does not coincide with the resonance frequency and Ls≠0, the control device 200 provides driving signals that have been calculated by using a and R obtained by the expressions (11) and (12) so as to drive the switches Qu, Qx, Qv, and Qy. As a result of driving the switches Qu, Qx, Qv, and Qy by these driving signals, the input power factor of the power receiving circuit 320 is controlled to be 1.
When other impedances have a great influence, for example due to a high wiring inductance, and the reference numeral 400 in FIG. 15 cannot be regarded as a pure resistance, a time period β is provided such that a reactance component included in the reference numeral 400 is also compensated for. As a result, the input power factor is set to 1.
In addition, when a waveform of v is the same as that in FIG. 14, the driving signals of the switches Qu, Qx, Qv, and Qy may be, for example, signals as illustrated in FIG. 16. Also in this case, by driving the switches Qu, Qx, Qv, and Qy by applying α and β obtained by the expressions (11) and (12), the input power factor of the power receiving circuit 320 can be set to 1.
However, the second prior application invention has the following problem.
Namely, in the second prior application invention, an induced voltage vin cannot be detected during the switching of the switches Qu, Qx, Qv, and Qy, and it is also difficult to calculate the induced voltage vin. Therefore, it is difficult to obtain a compensation period β for setting the input power factor to 1 from the theoretical expressions described above during the operation of a power supply device.